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A194390
Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(12) and < > denotes fractional part.
3
2, 4, 6, 8, 10, 12, 28, 30, 32, 34, 36, 38, 40, 56, 58, 60, 62, 64, 66, 68, 84, 86, 88, 90, 92, 94, 96, 112, 114, 116, 118, 120, 122, 124, 140, 142, 144, 146, 148, 150, 152, 168, 170, 172, 174, 176, 178, 180
OFFSET
1,1
COMMENTS
Every term is even; see A194368.
MATHEMATICA
r = Sqrt[12]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t1, 1]] (* empty *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]] (* A194390 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]] (* A194391 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 23 2011
STATUS
approved